Computation of symbolic dynamics for two-dimensional piecewise-affine maps

Lorenzo Sella; Pieter Collins

doi:10.3934/dcdsb.2011.15.739

Article Contents

2011, Volume 15, Issue 3: 739-767. Doi: 10.3934/dcdsb.2011.15.739

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Computation of symbolic dynamics for two-dimensional piecewise-affine maps

Lorenzo Sella^1, and
Pieter Collins^2,

1.
Niels Bohrweg 1, Leiden, 2333 CA
2.
Bouillonstraat 8-10, 6211 LH Maastricht

Received: June 2009

Revised: June 2010

Published: October 2011

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Abstract

In this paper we design and implement an algorithm for computing symbolic dynamics for two dimensional piecewise-affine maps. The algorithm is based on detection of periodic orbits using the Conley index and Szymczak decomposition of Conley index pair. The algorithm is also extended to deal with discontinuous maps. We compare the algorithm with the algorithm based on tangle of fixed points. We apply the algorithms to compute the symbolic dynamics and entropy bounds for the Lozi map.

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Mathematics Subject Classification: Primary: 37E99, 37B30, 37B40, 37B10.

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References

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